Uranium-238 decays via a longradioactive decay chain to eventually reach stable

Question

Uranium-238 decays via a longradioactive decay chain to eventually reach stable Pb-
206. The overall half life for this process is ~4.5 x109 years. U-208 in occurs meteorites,
within minerals such as zircon (ZrSiO4) in which a smallamount of U+4 was substituted in
place of Zr+4 when the mineral crystallized (Zr and Uhave the same +4 charge and are
of a similar size). Zircon will not, however, naturally accept Pb,due to its wrong chemical
valence (+2) and too-small size. So we can deduce that all thePb-206 present in the
meteorite zircon comes from the radioactive decay of uranium thathad been
incorporated when the zircon crystal formed. If a meteoritic zirconcurrently has 1000
ppm (parts-per-million) of U-238 and 1036 ppm of Pb-206, how old isthe meteorite

Explanation / Answer

Originally there must have been 1000 + 1036 = 2036 ppm ofU-238 and the fraction of U-238 remaining is 1000 / 2036 =.491 N = N0 e- t N / N0 = e- t = .491 ln .491 = - t = .693 / T1/2 = .693 / 4.5 * 10E9 = 1.54 *10E-10 -.711 = - 1.54 * 10E-10 * t t = 4.62 * 10E9 yrs N / N0 = e- t = .491 ln .491 = - t = .693 / T1/2 = .693 / 4.5 * 10E9 = 1.54 *10E-10 -.711 = - 1.54 * 10E-10 * t t = 4.62 * 10E9 yrs

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